Generalized Bhaskar Rao Designs with Block Size 4 Signed over Elementary Abelian Groups

Abstract

De Launey and Seberry have looked at the existence of Generalized Bhaskar Rao designs with block size 4 signed over elementary Abelian groups and shown that the necessary conditions for the existence of a $(v,4,\lambda ;EA(g))$ GBRD are sufficient for $\lambda >g$ with 70 possible basic exceptions. This article extends that work by reducing those possible exceptions to just a $(9,4,18h;EA(9h))$ GBRD, where $gcd(6,h)=1$, and shows that for $\lambda =g$ the necessary conditions are sufficient for $v>46$.